Measuring Instruments

1
Measuring Instruments

• Ruler
• 1 A ruler is used to measure lengths from a few
  cm up to 1 m. A metre rule has an accuracy of 0.1
  cm (i.e. 1 mm).

2
Measuring Instruments

• Ruler
• 2 Precautions to be taken when using a ruler
• (a) Ensure that the object is in contact with the
  ruler to avoid inaccurate readings.
• (b) Avoid parallax errors.

3
Measuring Instruments

• Ruler 
• Parallax errors in measurement arise as a result
  of taking a reading, with the eye of the observer
  in the wrong position with respect to the scale
  of the ruler. Figure 1.7 shows the correct
  position of the eye when reading the scale.

Error 0.1 cm
Error 0.1 cm
4
Measuring Instruments

• Ruler
• (c) Avoid zero and end errors.
• The ends of a ruler, which may be worn out, are a
  source of errors in measurement. Thus it is
  advisable to use the division mark 1' of the
  scale as the zero point when taking a measurement.

5
Measuring Instruments

• Ruler
• (c) Length of the block, l 3.2cm-1.0cm 2.2 cm

6
Measuring Instruments
Vernier Caliper

• 1 Lengths smaller than 1 mm can be measured with
  the help of an instrument called a vernier
  caliper. 

7
Measuring Instruments

• Vernier Caliper
•  2 A vernier caliper is used to measure an
  object with dimensions up to 12 cm with an
  accuracy of 0.01 cm.

8
Measuring Instruments

• Vernier Caliper
•  3 There are two pairs of jaws, one is designed
  to measure linear dimensions and external
  diameters while the other is to measure internal
  diameters.

9
Measuring Instruments

• Vernier Caliper
• 4. To measure with a vernier caliper, slide the
  vernier scale along the main scale until the
  object is held firmly between the jaws of the
  caliper. The subsequent steps are as follows.

10
Measuring Instruments

• Vernier Caliper
• (a)The reading on the main scale is determined
  with reference to the 0' mark on the vernier
  scale. The reading to be taken on the main scale
  is the mark preceding the Figure 1.10 shows that
  the '0' mark on the vernier scale lies between
  3.2 cm and 3.3 cm. The reading to be taken on the
  main scale is 3.2 cm (the 0' mark on the vernier
  scale acts as a pointer).

1
11
Measuring Instruments

• Vernier Caliper
• (b) The reading to be taken on the vernier scale
  is indicated by the mark on the vernier scale
  which is exactly in line or coincides with any
  main scale division line. Figure 1.10 shows that
  the fourth mark on the vernier scale is exactly
  in line with a mark on the main scale. Thus the
  second decimal reading of the measurement is
• Vernier scale reading 4 x 0.01 cm
• 0.04 cm

2
12
Measuring Instruments
0.04

• Vernier Caliper
•  
• (c) The reading of the vernier caliper is the
  result of the addition of the reading on the main
  scale to the reading on the vernier scale. 

3.2
13
Measuring Instruments
0.04

• Vernier Caliper
•  
• (c) The reading of the vernier caliper is the
  result of the addition of the reading on the main
  scale to the reading on the vernier scale.
• Caliper reading Main scale Reading Vernier
  scale reading
• Thus the reading of the vernier caliper in Figure
  1.10 is
• 3.2 0.04 3.24 cm

3.2
14
Measuring Instruments

• Vernier Caliper
• 5. A vernier caliper has a zero error if the 0'
  mark on the main scale is not in line with the
  '0' mark on the vernier scale when the jaws of
  the caliper are fully closed

15
Measuring Instruments

• Vernier Caliper
•   (a) Positive zero error
• Zero error 0.04 cm.
•  

16
Measuring Instruments
0.02cm
0.70 cm
0.72 cm
17
Measuring Instruments

• Vernier Caliper
• (b) Negative zero error
• Zero error -0.02 cm.

18
Measuring Instruments

• Micrometer Screw Gauge
•  
• 1 A micrometer screw gauge is used to measure
  small lengths ranging between 0.10 mm and 25.00
  mm.

19
Measuring Instruments

• Micrometer Screw Gauge
•  2 This instrument can be used to measure
  diameters of wires and thicknesses of steel
  plates to an accuracy of 0.01 mm.
•  

20
Measuring Instruments

• Micrometer Screw Gauge
•  
• 3 The micrometer scale comprises a main scale
  marked on the sleeve and a scale marked on the
  thimble called the thimble scale.

21
Measuring Instruments

• Micrometer Screw Gauge
•  4 The difference between one division on the
  upper scale and one division on the lower scale
  is 0.5 mm.
•  

22
Measuring Instruments

• Micrometer Screw Gauge
• 5 The thimble scale is subdivided into 50 equal
  divisions. When the thimble is rotated through
  one complete turn, i.e. 360?, the gap between the
  anvil and the spindle increases by 0.50 mm.
•  

23
Measuring Instruments

• Micrometer Screw Gauge
• 6 This means that one division on the thimble
  scale is 0.01 mm.

24
Measuring Instruments

• Micrometer Screw Gauge
• 7 When taking a reading, the thimble is turned
  until the object is gripped very gently between
  the anvil and the spindle.

25
Measuring Instruments

• Micrometer Screw Gauge
•  
• 8 The ratchet knob is then turned until a
  click' sound is heard.
•  

26
Measuring Instruments

• Micrometer Screw Gauge
• 9 The ratchet knob is used to prevent the user
  from exerting undue pressure.
•  

27
Measuring Instruments

• Micrometer Screw Gauge
• 10 The grip on the object must not be excessive
  as this will affect the accuracy of the reading.
•  

28
Measuring Instruments

• Micrometer Screw Gauge
• 11 Readings on the micrometer are taken as
  follows.
• (a) The last graduation showing on the main scale
  indicates position between 2.0 mm and 2.5 mm.
  Thus the reading on the main scale is read as 2.0
  mm.

29
Measuring Instruments

• Micrometer Screw Gauge
• 11 Readings on the micrometer are taken as
  follows.
• (b) The reading of the micrometer screw gauge is
  the sun of the main scale reading and the thimble
  scale reading which is
• 2.0 0.22 2.22 mm

30
Measuring Instruments

• Micrometer Screw Gauge
•  
• 11 Readings on the micrometer are taken as
  follows.
• (b) The reading on the thimble scale is the point
  where the horizontal reference line of the main
  scale is in line with the graduation mark on the
  thimble scale Figure 1.15(b) shows this to be the
  22nd mark on the thimble scale, thus giving a
  reading of 22 x 0.01 mm 0.22 mm.
•  

31
Measuring Instruments

• Micrometer Screw Gauge
• 12 Readings on the micrometer are taken as
  follows.
• (a) Positive zero error
• In Figure 1.16, the horizontal reference line in
  the main scale is in line with the 4th division
  mark, on the positive side of the 0' mark, on
  the thimble scale. The error of 0.04 mm must be
  subtracted from all readings taken.
• Zero error 0.04 mm
•  

32
Measuring Instruments

• Micrometer Screw Gauge
•  
• 13(b) Negative zero error
• In Figure 1.17, the horizontal reference line on
  the main scale is in line with the 3rd division
  mark, below the 0' mark of the thimble scale.
•  
• Zero error -0.03 mm
•  

33
Chapter 1

• 1.5 ANALYSING SCIENTIFIC INVESTIGATION

34
1.5 ANALYSING SCIENTIFIC INVESTIGATION

• 1. The investigative procedure begins with the
  following steps
•  
• Making an inference
• To interpret or explain what is being observed.
  It is also an early conclusion based on
  observation.

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1.5 ANALYSING SCIENTIFIC INVESTIGATION

• Determining the variables
• A variable is a physical quantity which
  varies/changes during the course of a scientific
  investigation. 

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1.5 ANALYSING SCIENTIFIC INVESTIGATION

• In a scientific investigation, there are 3
  different types of variables, namely
• (a) Manipulated variable
• It is a physical quantity which is fixed in an
  experiment.
• (b) Responding variable
• It is a physical quantity which depends on the
  independent variable.
• (c) Constant variable
• It is a physical quantity which is fixed while
  an experiment is being carried out.
•  

37
1.5 ANALYSING SCIENTIFIC INVESTIGATION

• Making a hypothesis
• It is a clarification/explanation regarding the
  relationship between the manipulated variable and
  the responding variable when all other variables
  are kept constant.
•  
• A hypothesis must be proven correct after an
  experiment is carried out.

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1.5 ANALYSING SCIENTIFIC INVESTIGATION

• Controlling the variable
• The experiment must be conducted in an
  appropriate place so as not to influence the
  variables.

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1.5 ANALYSING SCIENTIFIC INVESTIGATION

• Planning the investigative procedure/method
• Covers the choice and arrangement of the
  apparatus together with the work procedure being
  followed/ conducted.

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1.5 ANALYSING SCIENTIFIC INVESTIGATION

• Collecting data in tabular form
• Data in the same strips (i.e., rows and columns)
  must have the same units and the same number of
  decimal places (ie., data must be consistent).
•  
• For example

41
1.5 ANALYSING SCIENTIFIC INVESTIGATION

• 1. The investigative procedure begins with the
  following steps
•  
• Collecting data in tabular form
• For example

42
1.5 ANALYSING SCIENTIFIC INVESTIGATION

• Interpreting the data
• It is a result/decision that is made by way of
  the experiment.

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1.5 ANALYSING SCIENTIFIC INVESTIGATION

• Making a conclusion
• It is a record that is made regarding an
  information that is being studied based on the
  aim of the experiment.
• The conclusion which is made is based on the
  shape of the graph that is plotted and also on
  the value(s) of the quantities obtained through
  calculation using a formula.

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1.5 ANALYSING SCIENTIFIC INVESTIGATION

•  Making a complete report of an experiment
• A complete report of an experiment must cover all
  the following aspects
• Problem statement
• Inference
• Hypothesis
• Aim of experiment
• Variables of the experiment
• Arrangement of apparatus/Materials used

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1.5 ANALYSING SCIENTIFIC INVESTIGATION

•  Making a complete report of an experiment
• Experimental procedure - including the method
  for controlling the manipulated and responding
  variables.
• Tabulating data
• Analyzing data
• Making a conclusion
• Data tabulation
• Data analysis

46
1.5 ANALYSING SCIENTIFIC INVESTIGATION

• Experiment 1.1
• To Study The Relationship Between The Length Of A
  Pendulum And The Period Of Oscillation of The
  Pendulum
•  
• Problem Statement
• How can the period of oscillation of a pendulum
  be determined?
•  

47
1.5 ANALYSING SCIENTIFIC INVESTIGATION

• Experiment 1.1
• To Study The Relationship Between The Length Of A
  Pendulum And The Period Of Oscillation of The
  Pendulum
•  
• Hypothesis
• As the length of the pendulum increases, its
  period of oscillation increases.
•  

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1.5 ANALYSING SCIENTIFIC INVESTIGATION

• Variables
• (a) Manipulated Length of pendulum
• (b) Responding Period of oscillation
• (c) Constant Amplitude of oscillation, mass of
  pendulum bob (or weight) and acceleration due to
  gravity.

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1.5 ANALYSING SCIENTIFIC INVESTIGATION

• Experiment 1.1
• Apparatus/Materials Used
• Pendulum bob, a 100cm length of thread, metre
  rule, 2 small pieces of wood, retort stand and a
  stop-watch.
•  

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1.5 ANALYSING SCIENTIFIC INVESTIGATION

• Experiment 1.1
• To Study The Relationship Between The Length Of A
  Pendulum And The Period Of Oscillation of The
  Pendulum
• Procedure 

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1.5 ANALYSING SCIENTIFIC INVESTIGATION

• Experiment 1.1
• To Study The Relationship Between The Length Of A
  Pendulum And The Period Of Oscillation of The
  Pendulum
•  
• Procedure
• 1. A 50.0g pendulum bob is tied to one end of a
  100cm length thread.
• 2. By using a retort stand and two small pieces
  of wood, the other end of the thread is clamped
  as shown in Diagram 1.19.
• 3. The length, l of the pendulum is measured
  from the end below the small piece of wood to the
  centre of the bob. (i.e., l 20cm)
• 4. The pendulum is made to oscillate in a plane
  and having a small amplitude of oscillation.
  (i.e., approximately 10)

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1.5 ANALYSING SCIENTIFIC INVESTIGATION

• Procedure
• 5. The time taken to complete 20 full
  oscillations is recorded with a stop-watch.
• 6. The time for 20 complete oscillations is
  recorded once more.
• 7. The average time taken in the above two steps
  is calculated, so too with the time taken.
• 8. The experimental procedure is repeated by
  taking the length of the pendulum to be l 30cm,
  40cm, 50cm, 60 cm and 70cm.
• 9. All readings obtained are recorded in a
  table.
• 10. Then, a graph of T against l is plotted. 

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1.5 ANALYSING SCIENTIFIC INVESTIGATION

• Result
•  
•  

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1.5 ANALYSING SCIENTIFIC INVESTIGATION

• Graph T against L

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1.5 ANALYSING SCIENTIFIC INVESTIGATION

• Experiment 1.1
• Discussion
• Graph of period, T against length, L shows a
  curve with positive gradient. Thus, as L
  increases, T also increases. Hence, the
  hypothesis is accepted.

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1.5 ANALYSING SCIENTIFIC INVESTIGATION

• Conclusion
• The longer is the length of the pendulum, the
  longer is the period of its oscillation.